A291856 a(0) = -1, a(1) = 1, a(n) = a(n-1) + (n-1)*a(n-2) for n > 1.

-1, 1, 0, 2, 2, 10, 20, 80, 220, 860, 2840, 11440, 42680, 179960, 734800, 3254240, 14276240, 66344080, 309040160, 1503233600, 7374996640, 37439668640, 192314598080, 1015987308160, 5439223064000, 29822918459840, 165803495059840, 941199375015680

Offset: 0

Author

Seiichi Manyama, Sep 04 2017

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..800

Crossrefs

Cf. A000085, A000932, A249059.

Programs

GAP

a:=[-1,1];; for n in [3..10^2] do a[n]:=a[n-1]+(n-2)*a[n-2]; od; a;  # Muniru A Asiru, Sep 07 2017

Mathematica

RecurrenceTable[{a[0] == -1, a[1] == 1, a[n] == a[n-1] + (n-1)*a[n-2]}, a[n], {n, 0, 20}] (* Vaclav Kotesovec, Sep 04 2017 *)
CoefficientList[Series[E^(x*(2 + x)/2) * (E^(1/2)*Sqrt[2*Pi]*(Erf[(1 + x)/Sqrt[2]] - Erf[1/Sqrt[2]]) - 1), {x, 0, 20}], x]*Range[0, 20]! (* Vaclav Kotesovec, Sep 05 2017 *)

Formula

a(n+4) = 2*A249059(n) for n >= 0.

E.g.f.: exp(x*(2+x)/2) * (exp(1/2) * sqrt(2*Pi) * (erf((1+x)/sqrt(2)) - erf(1/sqrt(2))) - 1). - Vaclav Kotesovec, Sep 05 2017

a(n) ~ (sqrt(Pi) * exp(1/2) * (1 - erf(1/sqrt(2))) - sqrt(2)/2) * n^(n/2) * exp(sqrt(n) - n/2 - 1/4). - Vaclav Kotesovec, Sep 05 2017